This music is loud yet confidential. I cannot help feeling even more like the center of the universe than usual as I walk along to a rapid little version of "The Way You Look Tonight,"
The speaker gives us an overall sense of what this music sounds like here: it's "loud yet confidential." It's noisy and brash, but it's also intimate and secretive. It's a music that is full of contradiction—in a good way.
In this stanza the speaker also tells us what the music does to him: it makes him feel "even more/ like the center of the universe/ than usual." Of course, we all think we're the center of the universe. We see the world from our perspective and we want things to go our way.
But the music makes the speaker feel "even more" like the center of the universe. It makes him feel as if he's God, because if there is a center of the universe, "God" is as good a name for it as any.
The speaker's listening to a song, "The Way You Look Tonight," which was originally performed by Fred Astaire. It's a popular jazz standard.